Pancyclic graphs II
β Scribed by J.A Bondy; A.W Ingleton
- Book ID
- 103502595
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 293 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __D__ be an oriented graph of order __n__ β§ 9 and minimum degree __n__ β 2. This paper proves that __D__ is pancyclic if for any two vertices __u__ and __v__, either __uv__ β __A(D)__, or __d__~__D__~^+^(__u__) + __d__~__D__~^β^(__v__) β§ __n__ β 3.
In generalizing the concept of a pancyclic graph, we say that a graph is ''weakly pancyclic'' if it contains cycles of every length between the length of a shortest and a longest cycle. In this paper it is shown that in many cases the requirements on a graph which ensure that it is weakly pancyclic
We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and d G (x)+d G ( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C 3 ,